Related papers: Gibbs-non-Gibbs properties for evolving Ising mode…
In the present paper the Ising model with competing binary ($J$) and binary ($J_1$) interactions with spin values $\pm 1$, on a Cayley tree of order 2 is considered. The structure of Gibbs measures for the model considered is studied. We…
We consider $\mathbb Z$-valued $p$-SOS-models with nearest neighbor interactions of the form $|\omega_v-\omega_w|^p$, and finite-spin ferromagnetic models on regular trees. This includes the classical SOS-model, the discrete Gaussian model…
In this paper is studied HC-models on a Cayley tree. two states HC-model on a Cayley tree and Under some conditions on parameters of the two state HC-model we prove existence exactly two of the weakly periodic (non periodic) Gibbs measures.…
We consider a nearest-neighbor solid-on-solid (SOS) model, with several spin values $0,1,\ldots,m,$ $m\geq2,$ and nonzero external field, on a Cayley tree of degree $k$ (with $k+1$ neighbors). We are aiming to extend the results of…
In this paper we consider a $p$-adic Ising model on the Cayley tree of order $k\geq 2$. We give full description of all $p$-adic translation-invariant generalized Gibbs measures for $k=3$. Moreover, we show the existence of phase transition…
We consider the free boundary condition Gibbs measure of the Potts model on a random tree. We provide an explicit temperature interval below the ferromagnetic transition temperature for which this measure is extremal, improving older bounds…
We prove that at any inverse temperature $\beta$ and on any transitive amenable graph, the automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex combinations of the plus and minus states. This is obtained for a…
In this paper under some conditions on parameters of the Potts model with q-states on a Cayley tree of order k it is proved existence of the periodic (non translation-invariant)Gibbs measures. Also given a theorem about the number of these…
In the paper the Ising model with competing $J_1$ and $J_2$ interactions with spin values $\pm 1$, on a Cayley tree of order 2 (with 3 neighbors) is considered . We study the structure of the ground states and verify the Peierls condition…
We investigate the finite-state $p$-solid-on-solid model, for $p=\infty$, on Cayley trees of order $k\geq 2$ and establish a system of functional equations where each solution corresponds to a (splitting) Gibbs measure of the model. Our…
We consider the Curie-Weiss Potts model in zero external field under independent symmetric spin-flip dynamics. We investigate dynamical Gibbs-non-Gibbs transitions for a range of initial inverse temperatures beta<3, which covers the phase…
We study three Markov processes on infinite, unrooted, regular trees: the stochastic Ising model (also known as the Glauber heat bath dynamics of the Ising model), a majority voter dynamic, and a coalescing particle model. In each of the…
We consider Ising-spin systems starting from an initial Gibbs measure $\nu$ and evolving under a spin-flip dynamics towards a reversible Gibbs measure $\mu\not=\nu$. Both $\nu$ and $\mu$ are assumed to have a finite-range interaction. We…
We study the homogeneous nearest-neighbor Ising ferromagnet on the right half plane with a Dobrushin type boundary condition --- say plus on the top part of the boundary and minus on the bottom. For sufficiently low temperature $T$, we…
In this paper, we consider a Hard-Core $(HC)$ model with two spin values on Cayley trees. The conception of alternative Gibbs measure is introduced and translational invariance conditions for alternative Gibbs measures are found. Also, we…
We consider a version of the solid-on-solid model on the Cayley tree of order two in which vertices carry spins of value $0,1$ or $2$ and the pairwise interaction of neighboring vertices is given by their spin difference to the power $p>0$.…
We continue our study of Gibbs-non-Gibbs dynamical transitions. In the present paper we consider a system of Ising spins on a large discrete torus with a Kac-type interaction subject to an independent spin-flip dynamics…
Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs…
In the present paper we consider countable state $p$-adic Potts model on the Cayley tree. A construction of $p$-adic Gibbs measures which depends on weights $\l$ is given, and an investigation of such measures is reduced to examination of…
We study the Ising model on a Cayley tree. A wide class of new Gibbs states is exhibited.